Method and arrangement for testing the stability of a working point of a circuit

ABSTRACT

A DC transfer curve of a circuit is determined for determining the global dynamics of a circuit and a stability analysis is conducted for points of the DC transfer curve. The results of the stability analysis are at least one stable region and at least one unstable region of the DC transfer curve. This makes it possible to determine sensitivity, speed and process tolerance of the circuit.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a method and to an arrangement for checking astability of an operating point of a circuit.

2. Description of the Related Art

A circuit, particularly an analog electrical circuit (analog circuit),frequently contains inherent instabilities (unstable operating points,unstable points), which are purposefully utilized for meeting givenrequirements. An example is a current comparator, which compares areference current intensity with an input current intensity and sets anoutput voltage to one of two possible values depending on the differencebetween the two current intensities. Given this current comparator,there are two stable outside positions and one unstable middle position.The current comparator is based on the “flip-flop principle”.

It is generally of great interest to determine the stablity ofindividual operating points of the circuit. For this purpose, it isconventional to generate a system response to individual, localconfigurations and to evaluate it (see L. O. Chua et al.:“Computer-Aided Analysis of Electronic Circuits: Algorithms andComputational Techniques”, Prentice Hall, 1975 (Chua)). Only a localview of the dynamics of the circuit is received, and an extremelyintense calculation is required for an evaluation dependent on the timet.

A continuation method for determining a DC transfer curve for a circuitis known from U. Feldmann et al.: “Algorithms for Modern CircuitSimulation”, AEÜ, Vol. 46 (1992, No. 4, Hirzel-Verlag Stuttgart, pages274-285 (Feldmann).

On the basis of an eigenvalue method according to R. Neubert: “AnEffective Method for the Stability Analysis of Steady States in theSimulation of Large Electrical Networks”, In: W. Mathis & P. Noll(eds.), 2^(nd) ITG discussion: Neue Anwendungen theoretischer Konzeptein der Elektrotechnik, pages 41-48, Berlin, (4) 1995, ITG, VDE-Verlag.,a determination is made for an operating point of a circuit as towhether it is an asymptotically stable point (attractor) or an unstablepoint.

SUMMARY OF THE INVENTION

An object of the invention is to provide a method and an arrangement,which allows direct calculation of a global dynamic for a circuit.

This object is achieved by a method and an associated apparatus fordetermining a global dynamics of an electrical circuit, comprising thesteps of determining a DC transfer curve of the circuit; performing astability analysis for points of the DC transfer curve, the stabilityanalysis determining for each point whether each point is anasymptotically stable point or an unstable point; determining a stableregion of the DC transfer curve based on the asymptotically stablepoints; determining an unstable region of the DC transfer curve based onthe unstable points; and outputting global dynamics of the circuit basedon the stable region and the unstable region.

Further developments may include checking a stability of an operatingpoint by the allocation of the operating point to the closest stableregion of the DC transfer curve. The DC transfer curve may be determinedby a continuation method, and/or the stability analysis may be carriedout with an eigenvalue method. In the inventive method, the unstableregion may have a process tolerance which is directly proportional to asensitivity and indirectly proportional to a speed of the circuit, avariable group being defined by the process tolerance, the sensitivity,and the speed. The method may determine this sensitivity, speed, andprocess tolerance of the circuit. In the invention, the method mayfurther comprise the steps of fixing at least one of the variables inthe variable group; and dimensioning remaining unfixed variables in thevariable group based on the fixed variables. This method may be used todesign a comparator circuit (which may be a current comparator circuit)or a memory circuit. A functionality for designing circuits utilizing atleast one instability may be provided by the method. The elements of theinvention are explained in greater detail below.

For achieving this object, a method for determining a global dynamic ofa circuit is proposed, in which a DC transfer curve of the circuit isdetermined. A stability analysis is carried out for points of the DCtransfer curve that determines whether or not points of the DC transfercurve are asymptotically stable. Furthermore, at least one stable areaof the DC transfer curve and at least one unstable area of the DCtransfer curve are determined, where each area contains a series ofcoherent stable or unstable points. Therefore, the dynamics of thecircuit is determined by at least one stable area and at least oneunstable area. Coherent points are points of the same allocation“stable” or “unstable”.

On the basis of a successful determination of the (global) dynamics ofthe circuit, it is possible to determine a robustness of the circuit forindividual points (also: operating points), which are not situated onthe DC transfer curve. In an embodiment, an operating point isdetermined in that the operating point is allocated to the closeststable area of the DC transfer curve. In another embodiment, the DCtransfer curve is determined by continuation methods (see Feldmann).

The DC transfer curve contains a stationary state or a plurality ofstationary states dependent on a value occupancy of a parameter. For adynamic system

G(, v ,λ)=0  (1)

stationary solutions are determined in that the equation system

f( v , λ):=G(0, v , λ)=0(=0)  (2)

is solved, where

is a dynamic modification of a state vector,

v is a state vector and

λ is a parameter.

Such an equation system (2) can be solved by standard methods, such asNewton method (see Chua).

The continuation method makes it possible to determine a next point onthe DC transfer curve in that a next point is estimated in a directionalong a probable curve of the DC transfer curve, and this point servesas initial value for the equation (2). Subsequent to a number ofiterative steps, the correct next point results, which is actuallysituated on the DC transfer curve (at least within a prescribedapproximation).

In the framework of the stability analysis, the points of the DCtransfer curve are examined regarding their stability. On the basis ofthe eigenvalue method (see Neubert), in particular, asymptotic stabilityis checked preferably for each point or a fixed number of points on theDC transfer curve. Such a point is defined as an attractor. Theattractor is determined in that all points run toward it concerning thestability within a small environment around it. The attractor thereforerepresents a stable center for its immediate environment.

A separation of the stable outside positions by the unstable middleposition can result from the result of the stability analysis,particularly given comparator circuits.

Advantageously, the chronological dependencies of the circuit need notbe considered with respect to the described determination of the globaldynamics.

On the basis of a plurality of individual local output configurations,an integration (transient analysis) has previously been carried out. Theresult is interpreted by expert knowledge in order to be able to draw aconclusion regarding the sought global dynamics of the circuit. A timeexpenditure of up to 30 minutes can be expected for a transient analysis(for only one initial point), whereas it is possible to determine theglobal dynamics (without expert knowledge) by the method of the presentinvention in 10 minutes. Therefore, it is also possible to use themethod as preprocessing step, which is potentially followed by atransient analysis for individual points, which are of particularinterest.

In the framework of an additional embodiment, the unstable region canhave a process tolerance (ΔT), which is directly proportional to asensitivity (Δs) and indirectly proportional to a speed of the circuit.

In an embodiment or design of an (electrical) circuit, it isadvantageous to be able to represent all competing variables at once.Such competing variables are the speed of the circuit, the sensitivityand the process tolerance of the circuit (conditioned by theproduction). In a design phase of the circuit, specific values forspecific target variables are determined for a default in respectivecases. For example, the speed and the sensitivity of the circuit arecompeting targets; a compromise solution is determined between both.

In an embodiment of the invention, the described method is used fordesigning a comparator circuit, particularly a current comparatorcircuit. In another embodiment, the method is used for designing amemory circuit.

Generally, the described methods can be particularly utilized fordesigning circuits, in which at least one instability is used in orderto obtain a functionality. Given the current comparator, the instabilityis used in order to control a high output value (preferably a voltage)with a low current.

For achieving the invention, an arrangement for checking a stability ofan operating point of a circuit is also provided, which has a processorunit configured such that:

1) a DC transfer curve of the circuit can be determined;

2) a stability analysis can be carried out for points of the DC transfercurve, which determines whether or not each point is an asymptoticallystable point;

3) a stable region of the DC transfer curve contains the asymptoticallystable points and an unstable region of the DC transfer curve containsthe unstable points;

4) the global dynamics of the circuit are characterized by the at leastone stable region and the at least one unstable region.

This arrangement is particularly suitable for implementing the inventivemethod or one of its previously described further developments.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the invention are subsequently explained on thebasis of the drawings.

FIG. 1 is a block diagram illustrating input variables and outputvariables of a current comparator;

FIG. 2 is a graph representing a global dynamics of a circuit;

FIG. 3 is a graph representing a section from FIG. 2;

FIG. 4 is a graphic representation of an exemplary point that is notasymptotically stable;

FIG. 5 is a graphic representation of an exemplary point that isasymptotically stable (an attractor);

FIG. 6 is a block diagram representing steps for determining the globaldynamics of a circuit and application possibilities of these globaldynamics; and

FIG. 7 is a block diagram of a processor unit for implementing themethod.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 schematically shows a current comparator 101 comparing areference current I_(ref) to an input current I_(inp) and whichindicates the result of the comparison in the form of an output voltagev_(out). A control voltage v_(kontr) is provided for adjusting thecurrent comparator.

FIG. 2 shows the function principle of the current comparator. Thecurrent comparator 101 is based on the “flip-flop principle”, i.e.,respectively one stable outside position 202, 203, to which the outputvoltage v_(out) adjusts (indicated at the ordinate), is present outsideof an unstable middle position 201. Theoretically, v_(out) could alsoremain in the unstable middle position 201, but this is unlikely withrespect to a real technical system. Furthermore, a prediction of astable outside position 202 or 203 would no longer be possible foroperating points on the unstable middle position 201.

The circuit is adjusted by the control voltage v_(kont) close to theunstable middle position (v_(kontr) to “ready”). As a result of thecomparison of two current intensities I_(ref) and I_(inp), the outputvoltage v_(out) moves upward or downward into a stable outside position202 or 203. This movement is based on the non-linear dynamics of thecircuit, which passes into one of the two outside positions 202 or 203in a very fast and extremely sensitive manner.

The default movement of an operating point (e.g. one of the drawn points204 to 208) ensues in that a parameter λ (compare FIG. 2) is prescribedby which the non-linear dynamics of the circuit (shown by the course ofthe curve 202, 201 and 203) transfers the operating point into itsclosest stable outside position. It is thus possible to predict intowhich stable outside position 202 or 203 the respective operating pointpasses over. In the example of FIG. 2, the operating points 204 and 205are switched into the stable outside position 202; the operating points206, 207 and 208 are switched into the stable outside position 203.

In the example of the above-described current comparator, the parameterλ represents a difference I_(inp)−I_(ref) of the current intensityI_(inp) and of the reference current intensity I_(ref) to be compared.

The parameter λ represents an additional degree of freedom vis-à-vis asolution vector [v]. Since this solution vector [v] normally has adimension n, the dimension therefore derives as n+1 on the basis of theparameter λ. For representation purposes, the solution vector [v] can bereduced to a one-dimensional representation, for example by forming aEuclidian distance of its components.

FIG. 3 shows a section of the course of the curve 201 from FIG. 2. Realcircuits have a specific “unsharpness” in the region of their unstablemiddle position 201, this “unsharpness” being referred to as processtolerance 301. This process tolerance 301 results from the production ofthe circuit (fabrication tolerance). Particularly, physical dimensionsare a part of this process tolerance 301. The control voltage v_(kontr)prescribes a sensitivity 302 of the circuit. This sensitivity 302 isdetermined by the intersecting points of the limits of the processtolerance 301 with the control voltage v_(kont), where theseintersecting points are projected onto the abscissa. Another importantvariable is the speed of the circuit, for which the angle 303 betweenthe unstable middle position 201 and the control voltage v_(kontr) is ameasure (smaller angles correspond to higher speed).

In particular, the relationship

${{\Delta \quad s} \propto \frac{\Delta \quad T}{\sin \quad \alpha}},$

results with the following implications:

a) It is valid for a fixed speed (angle α=constant): The sensitivity isinversely proportional to the process tolerance ΔT is (the greater theregion Δs of the sensitivity on the abscissa in FIG. 3);

b) It is valid for a fixed process tolerance ΔT (=constant): The higherthe speed of the circuit (the smaller the angle α) the lower thesensitivity (the greater the region Δs); and

c) It is valid for a prescribed sensitivity (Δs=constant): The greaterthe process tolerance ΔT, the lower the speed of the circuit (thegreater the angle α is).

Therefore, a plurality of targets derive, which compete with one anotherand which must be weighed against one another in the framework of acircuit design (design of a circuit). Special defaults are met by anappropriate selection of a process tolerance 301. The responsible designspecialist must evaluate this on an individual basis for eachapplication case.

FIG. 2 shows the course of the curve of the global dynamics of anunderlying circuit, where each point on this curve is differentiated asto whether it is an asymptotically stable point (see curve sections 202and 203) or an unstable point (unstable middle position 201). FIG. 4shows an example for a point 401 that is not asymptotically stable. Inan immediate environment 402 of this point, there are points that runtoward to this point 401, e.g. the points on the axis sections 403 and405. However, there are also points, namely on the axis sections 404 and406, which run away from the point 401. Therefore, the point 401 is notasymptotically stable. On the other hand, FIG. 5 shows a point 501, inwhose immediate environment 502 all points run toward this point. Point501 therefore is an attractor.

FIG. 6 shows a block flow diagram comprising steps for determining theglobal dynamics of a circuit and utilization possibilities of thisglobal dynamics. In a step 601, the DC transfer curve is determined by acontinuation method (see Feldmann). Each point or a fixed quantity ofpoints on the DC transfer curve are subjected to a stability analysis(see Neubert; see step 602), to determine whether the point(s) areattractors. Coherent attractors represent a stable outside position andcoherent points, which are not attractors, represent the unstable middleposition. This results in a course of the curve, which comprises stableoutside positions and an unstable middle position and which marks theglobal dynamics of the underlying circuit (see step 603). Operatingpoints that are not situated exactly on the unstable middle positionwill assume the closest stable outside position as a stable finalcondition. In this way, it is possible to determine the stability of anoperating point (step 604). Furthermore, a circuit design according tothe statements of the global dynamics is alternatively suitably adaptedto the circuit, so that specific defaults are met.

FIG. 7 shows a processor unit PRZE. The processor unit PRZE comprises aprocessor CPU, a memory MEM and an input/output interface IOS, which isused in different ways via an interface IFC: An output becomes visibleat a monitor MON via a graphic interface and/or is outputted on aprinter PRT. Inputs occur via a mouse MAS or a keyboard TAST. Theprocessor unit also comprises a data bus BUS assuring the connection ofa memory MEM, the processor CPU and of the input/output interface IOS.Furthermore, additional components can be connected to the data bus BUS,e.g. additional memory, data memory (hard disk), or scanner.

The above-described method and apparatus are illustrative of theprinciples of the present invention. Numerous modifications andadaptations will be readily apparent to those skilled in this artwithout departing from the spirit and scope of the present invention.

Bibliography

[1] U. Feldmann et al.: “Algorithms for Modern Circuit Simulation”, AEÜ,Vol. 46 (1992, No. 4, Hirzel-Verlag Stuttgart, pages 274-285.

[2] R. Neubert: “An Effective Method for the Stability Analysis ofSteady States in the Simulation of Large Electrical Networks”, In: W.Mathis & P. Noll (eds.), 2^(nd) ITG discussion: Neue Anwendungentheoretischer Konzepte in der Elektrotechnik, pages 41-48, Berlin, (4)1995, ITG, VDE-Verlag.

[3] L. O. Chua et al.: “Computer-Aided Analysis of Electronic Circuits:Algorithms and Computational Techniques”, Prentice Hall, 1975.

What is claimed is:
 1. A method for determining a global dynamics of anelectrical circuit, comprising the steps of: determining a DC transfercurve of said circuit; performing a stability analysis for points ofsaid DC transfer curve, said stability analysis determining for eachpoint whether each point is an asymptotically stable point or anunstable point; determining a stable region of said DC transfer curvebased on said asymptotically stable points; determining an unstableregion of said DC transfer curve based on said unstable points; andoutputting global dynamics of said circuit based on said stable regionand said unstable region.
 2. The method according to claim 1, furthercomprising the step of: checking a stability of an operating point bythe allocation of said operating point to the closest stable region ofsaid DC transfer curve.
 3. The method according to claim 1, wherein saidDC transfer curve is determined by a continuation method.
 4. The methodaccording to claim 1, wherein said stability analysis is carried outwith an eigenvalue method.
 5. The method according to claim 1, whereinsaid unstable region has a process tolerance which is directlyproportional to a sensitivity and indirectly proportional to a speed ofsaid circuit, a variable group being defined by said process tolerance,said sensitivity, and said speed.
 6. The method according to claim 5,further comprising the step of determining said sensitivity, speed, andprocess tolerance of said circuit.
 7. The method for designing a circuitaccording to claim 1, further comprising the steps of: fixing at leastone of the variables in said variable group; and dimensioning remainingunfixed variables in said variable group based on said fixed variables.8. The method according to claim 1, further comprising the step ofdesigning a comparator circuit utilizing said global dynamics.
 9. Themethod according to claim 8, wherein said comparator circuit is acurrent comparator circuit.
 10. The method according to claim 1, furthercomprising the step of designing a memory circuit utilizing said globaldynamics.
 11. The method according to claim 1, further comprising thestep of obtaining a functionality for designing circuits utilizing atleast one instability.
 12. An arrangement for checking a stability of anoperating point of a circuit, comprising: a processor unit thatcomprises a processor, said processor unit being configured to:determine a DC transfer curve of said circuit; perform a stabilityanalysis that is carried out for points of the DC transfer curve, saidstability analysis determining for each point whether each point is anasymptotically stable point or an unstable point; determine a stableregion of said DC transfer curve based on said asymptotically stablepoints; determine an unstable region of said DC transfer curve based onsaid unstable points; and characterizing global dynamics of said circuitbased on said stable region and said unstable region.